Asymptotic analysis of quasi-steady n-heptane droplet combustion supported by cool-flame chemistry

Abstract

A skeletal chemical-kinetic mechanism for n-heptane cool flames is simplified to the maximum extent possible by introduction of steady-state approximations for intermediaries, following procedures employed previously in addressing two-stage ignition. A pair of ordinary differential equations in mixture-fraction space is thereby obtained, describing the quasi-steady structures of the temperature and heptylketohydroperoxide fields. Application of activation-energy asymptotics for the partial-burning regime to this pair of equations is shown to provide convenient expressions for flame structures and the extinction condition associated with maximally reduced chemistry. With the mixture-fraction co-ordinate related to radius, these results are used to address droplet-combustion experiments that have been performed in the International Space Station. Droplet diameters at extinction are predicted as functions of the oxygen concentration in the atmosphere and are compared with experiment. While the results are encouraging concerning qualitative predictions of dependences of extinction diameters on atmospheric conditions, there are noticeable quantitative differences that point to deficiencies in the analysis, likely resulting from a number of oversimplifications. Further investigation is therefore recommended.

Keywords:

• asymptotic analysis
• partial burning regime
• cool flames
• droplet combustion
• extinction

Acknowledgements

We are especially pleased to be able to submit our contribution to this birthday celebration issue for Grisha Sivashinsky because of his numerous seminal advances in our understanding of combustion science.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. This Lewis number will, in fact, be appreciably greater than unity, and, in addition, there are experimental indications that Soret diffusion is important quantitatively [13]. These effects contribute to the inaccuracy of the results of the present analysis, which represents only a first step towards the development of an understanding of the phenomenon. These approximations are shared by our earlier analysis [15] where further discussion may be found.

Additional information

Funding

The research at the University of California at San Diego (UCSD) was supported by the National Aeronautics and Space Administration (NASA) microgravity science program, and by the National Science Foundation [award #CBET-1404026].